When to use: Size shallow footings (spread, strip, mat) by computing the soil's ultimate bearing capacity. Uses Terzaghi's equation qu = c·Nc + q·Nq + 0.5·γ·B·Nγ with shape factors for strip, square, and circular footings. The bearing capacity factors Nc, Nq, and Nγ are functions of the soil friction angle φ. Allowable bearing = qu / FS (default FS = 3). Account for the groundwater table, which reduces effective unit weight and bearing capacity.
Shallow foundation bearing capacity is one of the most fundamental calculations in geotechnical engineering. It determines the maximum load per unit area that a soil can support without undergoing shear failure, and it is the primary basis for sizing spread footings, strip footings, and mat foundations. This calculator implements Terzaghi's general bearing capacity equation with shape factors for strip, square, and circular footings, applying water table corrections per established geotechnical practice.
Karl Terzaghi (1943) formulated the first comprehensive bearing capacity equation for shallow foundations. The general form is:
qu = c·Nc·sc + q·Nq + 0.5·γ·B·Nγ·sγ
where c is cohesion (kPa), q is the effective overburden pressure at the footing base (γ·Df), γ is the soil unit weight, B is the footing width, and Nc, Nq, Nγ are dimensionless bearing capacity factors that depend solely on the soil friction angle φ. The factors are derived from plasticity theory: Nq = e^(π·tanφ)·tan²(45+φ/2), Nc = (Nq−1)·cotφ, and Nγ = 2(Nq+1)·tanφ (Vesic expression). For purely cohesive soil (φ = 0, undrained analysis), Nc = 5.14 and Nq = 1.0, the classic result from the plasticity solution.
The ultimate bearing capacity (qu) represents the soil pressure at which general shear failure initiates. In practice, foundations are designed to a net allowable bearing capacity (qa = qu/FS) where FS is the factor of safety. The standard factor of safety for bearing capacity is 3.0 for most permanent structures under normal loading conditions. This accounts for uncertainties in soil properties, load variability, and the distinction between general and local shear failure modes.
For settlement-sensitive structures, the allowable bearing capacity may be further reduced below qu/3 so that settlements remain within tolerable limits. In many cases, settlement — not bearing capacity failure — governs the foundation design, particularly for fine-grained soils.
Foundation depth (Df) increases bearing capacity through the surcharge term q·Nq: the overburden pressure at the footing base acts as a confining stress that suppresses failure. Embedding a footing deeper into a strong stratum also bypasses weaker near-surface soils.
Foundation width (B) affects the width term 0.5·γ·B·Nγ: wider footings mobilize more soil mass in the failure mechanism, increasing ultimate capacity — but also increasing the depth of the pressure bulb and therefore the settlement. For cohesive soils (φ ≈ 0), width has little effect on ultimate bearing capacity since Nγ → 0, but it governs consolidation settlement.
Bearing capacity varies enormously with soil type. Dense gravels and well-compacted granular fills can sustain 300–600 kPa allowable. Medium-dense sands typically support 100–300 kPa. Stiff clays (Su = 50–100 kPa) yield allowable bearing values of 100–200 kPa. Soft clays (Su < 25 kPa) may only support 25–75 kPa and often require deep foundations. Rock, depending on type and weathering, can sustain thousands of kPa.
These ranges assume a factor of safety of 3 and no groundwater effects. The USCS soil classification group symbol is a useful starting point for estimating likely bearing capacity ranges before laboratory data are available.
Sandy soils, particularly dense sands and gravels, typically have allowable bearing capacities of 150–400+ kPa for shallow footings (using FS = 3). Clayey soils are more variable: stiff to very stiff clays (undrained shear strength Su = 50–150 kPa) can support 100–250 kPa, while soft clays (Su < 25 kPa) may only allow 25–75 kPa. The critical difference is that sand behavior is drained (pore pressures dissipate quickly) while clay under rapid loading is undrained, meaning the full friction angle is not available and the analysis uses a total-stress undrained shear strength.
A factor of safety of 3.0 on ultimate gross bearing capacity is standard for most permanent structures. This accounts for uncertainty in soil parameters, load variability, and spatial variability of soil conditions. A lower FS of 2.0–2.5 may be acceptable for temporary structures, when soil properties are well-characterized by extensive testing, or when the consequence of failure is low. Some codes distinguish between the gross FS (applied to qu) and the net FS (applied to qu minus the overburden). Always verify that the FS applied is consistent with how the bearing capacity was calculated.
A high groundwater table reduces bearing capacity by lowering the effective unit weight of soil below the water table. The submerged (buoyant) unit weight is approximately γ - γw ≈ γ - 9.81 kN/m³, roughly half the bulk unit weight. This affects both the surcharge term q (when the water table is above the footing base) and the width term γ·B·Nγ (when the water table is within B below the footing base). In the worst case — water table at the ground surface — bearing capacity can be reduced by 30–50% compared to the dry condition. The calculator applies these corrections automatically based on the water table depth input.
The gross ultimate bearing capacity (qu) is the total soil pressure at failure, including the existing overburden stress at the footing level. The net ultimate bearing capacity (qu,net = qu - q) excludes the overburden, representing only the additional stress the soil can carry beyond what it already carries. The net allowable bearing capacity (qa,net = qu,net/FS) is useful when comparing against the net structural load on the soil (column load / footing area minus the weight of soil excavated). In most practical cases, engineers work with gross bearing capacity but should be consistent in comparing it against gross applied pressures.
Deep foundations (piles, drilled shafts, micropiles) are warranted when: (1) the near-surface soils are too weak or compressible to support the structural loads, (2) there is a deep competent stratum that can be reached by the deep foundation, (3) the structure is sensitive to differential settlement, (4) scour or frost penetration depth makes a shallow footing vulnerable, or (5) significant lateral loads or uplift forces must be resisted. A common rule of thumb is that shallow footings become uneconomical when the required footing width exceeds the depth by a ratio greater than about 2:1, or when expected settlement under allowable bearing pressure exceeds tolerable limits.